Ceva, Giovanni
,
Geometria motus
,
1692
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homogeneæ ipſæ imagines, ſi vt ex Def. 4. huius IL ad HF
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erit vt velocitas inſtanti I ad velocitatem mobilis inſtanti
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F) Dico ſpatium AB ad DE eſſe vt imago rectangulum̨
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ILMK ad imaginem rectangulum FHNG. </
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ipſa illa rectangula ex ratione altitudinum IK ad FG, & ex
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ea baſium IL ad FH; verùm ex ijſdem, ea nempe
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IK ad FG, atque ea velocitatum IL ad FH componitur
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etiam ratio ſpatiorum AB ad DE, ergo ipſa ſpatia erunt vt
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propoſitę imagines.
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Tab.
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1.
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Fig.
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9.
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Cor. </
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3.
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huius.
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Gil. de motu
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æquabili.
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Tab.
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1.
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fig
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10.</
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<
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">2. Sint nunc motus iuxta imagines, quarum altera acu
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minata, altera rectangulum ſit. </
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quod curritur iuxta imaginem ABCD ad ſpatium DE,
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quod curritur iuxta alteram imaginem, eſſe vt imago
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ABCD ad imaginem PHNG. </
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tudo Y maior, vel minor imagine ABCD, quæ quidem ad
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alteram imaginem HPGN habebit eandem rationem,
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ſpatium AB ad DE. </
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cumſcribatur; vt egimus in ſecunda parte primæ huius, fi
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gura imagini ABCD conſtans ex rectangulis æquè altis,
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excedatque imaginem ABCD exceſſu minori, quam Z; ſit
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ergo circumſcripta illa AE, HF, IG, KG, quam primò fa
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cilè oſtendemus minorem magnitudine Y; nam hæc exceſ
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ſu magis diſtat ab imagine, quàm circumſcripta illa. </
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terea ſi intelligantur tot motus æquabiles, quot ſunt
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circumſcripta, ij nempe, qui fierent temporibus AH,
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HI, IK, KD iuxta deinceps imagines ipſa rectangula AE,
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HF, IG, KC interſe, & propoſitis imaginibus homogeneas,
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velocitates, quibus ijdem motus conſiderarentur, forent
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HE, IF, KG, DC, nimirum maximæ imaginum ABEH,
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HEFI, IFGK, KGCD; Cumque ita ſit, longiora ſpatia cur</
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rerentur iuxta imagines rectangula circumſcripta, quam
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ijſdem temporibus, imaginibuſque poſtremis, hoc eſt
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tempore AD iuxta imaginem ABCD; obidque ſpatium
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AB ad DE, ſeu magnitudo Y ad imaginem HPGN habe-</
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